Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 1

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 2

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 3

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 4

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 5

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 6

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 7

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 8

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 9

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 10

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

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eSolutions Manual - Powered by Cognero Page 11

Mid-Chapter Quiz

Translate each sentence into an equation.�

���The sum of three times a and four is the same as five times a.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The sum of three times a and four is the same as five times a is the same as three times a plus four equals five times a. �

�

three times a

number a �

plus four equals five times

a number

a 3a + 4 = 5a

The equation is 3a + 4 = 5a.

���One fourth of m minus six is equal to two times the sum of m and 9.

62/87,21���5HZULWH�WKH�YHUEDO�VHQWHQFH�VR�LW�LV�HDVLHU�WR�WUDQVODWH��One fourth of m minus six is equal to two times the sum of m and 9 is the same as 2QH�IRXUWK�WLPHV�P�PLQXV�VL[�LV�HTXDO�WR�WZR�WLPHV�WKH�TXDQWLW\��P�SOXV��� �

� The equation is .

one fourth of m minus six equals

two times the

quantity m plus 9

± 6 = 2(m + 9)

���The product of five and w is the same as w to the third power.

62/87,21���Rewrite the verbal sentence so it is easier to translate. The product of five and w is the same as w to the third power is the same as five times w equals w to the third power . �

�

five times w equals w to the third power 5 � w = w3

The equation is 5w = w3.

���MARBLES 'UHZ�KDV����UHG��JUHHQ�DQG�EOXH�PDUEOHV���+H�KDV�VL[�PRUH�UHG�PDUEOHV�WKDQ�EOXH�PDUEOHV�DQG�IRXU�fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

62/87,21���To write the equation, let b = the number of blue marbles. Express the other colors in terms of b.�

� The equation is 3b + 2 = 50. �

� Drew has 16 blue marbles.

Six more red than

blue

and four fewer green than

blue

plus blue equals 50

b + 6 + b ± 4 + b = 50

Solve each equation. Check your solution.���p + 8 = 13

62/87,21���

Check:

���±26 = b ± 3

62/87,21���

Check:

��� = 3

62/87,21���

Check:

���MULTIPLE CHOICE Solve the equation .

A

B ��

C �

D �±3

62/87,21���

Choice C is the correct answer.

Solve each equation. Check your solution.���2x + 5 = 13

62/87,21���

Check:

����±21 = 7 ± 4y

62/87,21���

Check:

����

62/87,21���

Check:

�����

62/87,21���

Check:

����FISH The average length of a yellow±banded angelfish is 12 inches. This is 4.8 times as long as an average common goldfish. a. Write an equation you could use to find the length of the average common goldfish. b. What is the length of an average common goldfish?

62/87,21���a. To write the equation, let g = the length of the average common goldfish. �

�

length of yellow-banded

angelfish

is 4.8 times as long as an average common goldfish

12 = 4.8 � g

The equation is 12 = 4.8g. b.

� The length of the average common goldfish is 2.5 inches.

Write an equation and solve each problem.����Three less than three fourths of a number is negative 9. Find the number.

62/87,21���To write the equation, rewrite the sentence and let n represent the unknown number. Three less than three fourths of a number is negative 9 is the same as three fourths of a number minus three is negative 9. �

� The equation is . �

� The number is ±8.

Three fourths �

of a number minus three is negative 9.

� n ± 3 = ±9

����Thirty is twelve added to six times a number. What is the number?

62/87,21���To write the equation, let n represent the unknown number. �

�

Thirty is twelve added to six times a number.

30 = 12 + 6 � n

The equation is 30 = 12 + 6n. �

� The number is 3.

����Find four consecutive integers with a sum of 106.

62/87,21���To write the equation, rewrite the sentence and let n = the first of the four unknown numbers. Then the next three consecutive integers are n + 1, n + 2, and n + 3. The sum of these four integers equals 106, so the equation is n + (n + 1) + (n + 2) + (n + 3) = 106. Solve for n. �

� Substitute 25 for n to find remaining three numbers. n + 1 = 25 + 1 or 26 n + 2 = 25 + 2 or 27 n + 3 = 25 + 3 or 28 � The four consecutive integers are 25, 26, 27, and 28.

Solve each equation. Check your solution.����8p + 3 = 5p + 9

62/87,21���

Check:

����

62/87,21���

Check:

����

62/87,21���

Check:

����PERIMETER Find the value of x so that the triangles have the same perimeter.

62/87,21���To write the equation, write an expression for each perimeter. Set the expressions equal to each other: 5 + (x ± 5) + (x ± 4) = 16 + 10 + (x ± 10). �

� When x = 20, the triangles have the same perimeter.

����PRODUCTION ABC Sporting Goods Company produces baseball gloves. Their fixed monthly production cost is $8000 with a per glove cost of $5. XYZ Sporting Goods Company also produces baseball gloves. Their fixed monthlyproduction cost is $10,000 with a per glove cost of $3. Find the value of x, the number of gloves produced monthly, so that the total monthly production cost is the same for both companies.

62/87,21���7R�ZULWH�WKH�HTXDWLRQ��ZULWH�DQ�H[SUHVVLRQ�IRU�WKH�SURGXFWLRQ�FRVW�IRU�HDFK�FRPSDQ\�� � For ABC Sporting goods, their monthly fixed cost is $8000 and per glove (variable) cost of $5. Total cost for ABC is the total of the fixed and variable costs. Thus for ABC, Total cost = 8000 + 5x�� � For XYZ Sporting goods, their monthly fixed cost is $10,000 and per glove (variable) cost of $3. Total cost for XYZ is the total of the fixed and variable costs. Thus for XYZ, Total cost = 10,000 + 3x�� � Set the expressions equal to each other. The equation is 8000 + 5x = 10,000 + 3x. �

� If each company produces 1000 gloves, their total monthly production cost will be the same.

Evaluate each expression if x = ±4, y = 7, and z = ±9.����|3x ± 2| + 2y

62/87,21���

����|±4y + 2z | ± 7z

62/87,21���

����MULTIPLE CHOICE Solve |6m ± 3| = 9. F {2} G {±1, 2} H {±3, 6} J {±3, 3}

62/87,21���Case 1:

� Case 2:

� The solution set is {±1, 2}. Choice G is correct.

����COFFEE 6RPH�VD\�WR�EUHZ�DQ�H[FHOOHQW�FXS�RI�FRIIHH��\RX�PXVW�KDYH�D�EUHZLQJ�WHPSHUDWXUH�RI������)��SOXV�RU�minus 5 degrees. Write and solve an equation describing the maximum and minimum brewing temperatures for an excellent cup of coffee.

62/87,21���To write the equation, let t = the temperature of an excellent cup of coffee. Case 1: t ± 200 = 5 Case 2: t ± 200 = ±5 The equation is |t ± 200| = 5. � Case 1:

� Case 2:

� 7KH�PD[LPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�DQG�WKH�PLQLPXP�EUHZLQJ�WHPSHUDWXUH�LV�����)�

eSolutions Manual - Powered by Cognero Page 12

Mid-Chapter Quiz